Difference between revisions of "2004 AMC 10A Problems/Problem 7"
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==Problem== | ==Problem== | ||
| − | A grocer stacks oranges in a pyramid-like stack whose rectangular base is 5 oranges by 8 oranges. Each orange above the first level rests in a pocket formed by four oranges below. The stack is completed by a single row of oranges. How many oranges are in the stack? | + | A grocer stacks oranges in a pyramid-like stack whose rectangular base is <math>5</math> oranges by <math>8</math> oranges. Each orange above the first level rests in a pocket formed by four oranges below. The stack is completed by a single row of oranges. How many oranges are in the stack? |
| − | <math> \mathrm{(A) \ } 96 \qquad \mathrm{(B) \ } 98 \qquad \mathrm{(C) \ } 100 \qquad \mathrm{(D) \ } 101 | + | <math> \mathrm{(A) \ } 96 \qquad \mathrm{(B) \ } 98 \qquad \mathrm{(C) \ } 100 \qquad \mathrm{(D) \ } 101 \qquad \mathrm{(E) \ } 134 </math> |
==Solution== | ==Solution== | ||
| − | There are <math>5\times8=40</math> oranges on the | + | There are <math>5\times8=40</math> oranges on the <math>1^{\text{st}}</math> layer of the stack. The <math>2^{\text{nd}}</math> layer that is added on top of the first will be a layer of <math>4\times7=28</math> oranges. When the third layer is added on top of the <math>2^{\text{nd}}</math>, it will be a layer of <math>3\times6=18</math> oranges, etc. |
| − | Therefore, there are <math>5\times8+4\times7+3\times6+2\times5+1\times4=40+28+18+10+4=100</math> oranges in the stack <math>\ | + | Therefore, there are <math>5\times8+4\times7+3\times6+2\times5+1\times4=40+28+18+10+4=100</math> oranges in the stack. <math>\boxed{\mathrm{(C)}\ 100}</math> |
| − | |||
| − | + | ==Video Solution== | |
| + | https://youtu.be/H2OQPsSWG4A | ||
| − | + | Education, the Study of Everything | |
| − | + | == See also == | |
| + | {{AMC10 box|year=2004|ab=A|num-b=6|num-a=8}} | ||
[[Category:Introductory Algebra Problems]] | [[Category:Introductory Algebra Problems]] | ||
| + | {{MAA Notice}} | ||
Latest revision as of 00:14, 12 April 2022
Contents
Problem
A grocer stacks oranges in a pyramid-like stack whose rectangular base is 
oranges by 
oranges. Each orange above the first level rests in a pocket formed by four oranges below. The stack is completed by a single row of oranges. How many oranges are in the stack?
Solution
There are 
oranges on the 
layer of the stack. The 
layer that is added on top of the first will be a layer of 
oranges. When the third layer is added on top of the , it will be a layer of 
oranges, etc.
Therefore, there are 
oranges in the stack. 
Video Solution
Education, the Study of Everything
See also
| 2004 AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by Problem 6 |
Followed by Problem 8 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AMC 10 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
